The Collaborative International Dictionary of English v.0.48:

Tangent \Tan"gent\, a. [L. tangens, -entis, p. pr.]
   Touching; touching at a single point; specifically (Geom.)
   meeting a curve or surface at a point and having at that
   point the same direction as the curve or surface; -- said of
   a straight line, curve, or surface; as, a line tangent to a
   curve; a curve tangent to a surface; tangent surfaces.
   [1913 Webster]

   Tangent plane (Geom.), a plane which touches a surface in a
      point or line.

   Tangent scale (Gun.), a kind of breech sight for a cannon.


   Tangent screw (Mach.), an endless screw; a worm.
      [1913 Webster]
      [1913 Webster]

WordNet (r) 3.0 (2006):

tangent plane
    n 1: the plane that contains all the lines tangent to a specific
         point on a surface